Question

The table below gives the list price and the number of bids received for five randomly selected items sold through online auctions. Using this data, consider the equation of the regression line, yˆ=b0+b1xy^=b0+b1x, for predicting the number of bids an item will receive based on the list price. Keep in mind, the correlation coefficient may or may not be statistically significant for the data given. Remember, in practice, it would not be appropriate to use the regression line to make a prediction if the correlation coefficient is not statistically significant.

Price in Dollars	22	33	35	40	45
Number of Bids	2	3	4	6	7

Step 1 of 6:

Find the estimated slope. Round your answer to three decimal places.

Step 2 of 6: Find the estimated y-intercept. Round your answer to three decimal places.

Step 3 of 6: Find the estimated value of y when x = 40. Round your answer to three decimal places.

Step 4 of 6: Determine the value of the dependent variable yˆ at x = 0.

Step 5 of 6: Substitute the values you found in steps 1 and 2 into the equation for the regression line to find the estimated linear model. According to this model, if the value of the independent variable is increased by one unit, then find the change in the dependent variable yˆ.

Step 6 of 6: Find the value of the coefficient of determination. Round your answer to three decimal places.

Answer 1

The given data is as follows:

No
1	22	2	484	44	4
2	33	3	1089	99	9
3	35	4	1225	140	16
4	40	6	1600	240	36
5	45	7	2025	315	49

Step 1)

Using the last row of the above table, we can now calculate the slope b1 first.

Step 2)

The intercept b0 is calculated using the same row as well as b1.

Step 3)

When x=40, we have:

Step 4)

When x=0, we have the intercept as the value:

Step 5)

The estimated model is:

When x increases by 1, correspondingly increases by .

Step 6)

The coefficient of determination is calculated from the same row as:

Note that is always between 0 and 1. Here, is close to 1, so the regression model is appropriate.